Mathematician Maryam Mirzakhani is the first woman to win a Fields Medal. It had been an all-boys club since the prizes were established in 1936. Mirzakhani, a native of Iran, is a professor at Stanford University. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.” Here’s how Nature summed up her contributions:
"Perhaps Maryam’s most important achievement is her work on dynamics," says Curtis McMullen of Harvard University. Many natural problems in dynamics, such as the three-body problem of celestial mechanics (for example, interactions of the Sun, the Moon and Earth), have no exact mathematical solution. Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems’ trajectories “are tightly constrained to follow algebraic laws”, says McMullen. He adds that Mirzakhani’s achievements "combine superb problem-solving ability, ambitious mathematical vision and fluency in many disciplines, which is unusual in the modern era, when considerable specialization is often required to reach the frontier".
Erica Klarreich wrote a wonderful summary of Dr. Mirzakhani for Quanta magazine, which is worth a read. She’s apparently quite the generalist—deriving intellectual satisfaction in “crossing the imaginary boundaries people set up between different fields.” Among her diverse body of work outside dynamics is her doctoral dissertation on geodesics of hyperbolic surfaces, which another researcher called “the kind of mathematics you immediately recognize belongs in a textbook.” Meanwhile, she’s an unassuming character herself, with a deep love of her work and a phenomenal work ethic: "You have to spend some energy and effort to see the beauty of math."